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Abstract
This paper presents the first semi-analytic solution of two-phase two-component compressible flow in permeable media using method of characteristics (MOC). Analytical solutions are important as numerical simulations do not yield explicit expressions in terms of the model parameters. However, the previously developed MOC solutions rely on the incompressible fluid and rock assumptions that are rarely met in practice Furthermore, numerical simulations that provide the most comprehensive solutions to multiphase flow problems are computationally intensive. In this study, the method of characteristics (MOC) solution of the overall mass conservation equation of CO2 in two-phase two-component flow through permeable media is derived with no restriction on the compressibility of fluids and the rock.

A simulation approach is used to verify the derived analytical solutions. The simulation models consist of a vertical injection well and a producer located at the ends of a one-dimensional (1D) grid. The pace at which specific gas saturations propagate along the permeable medium are compared with the gas saturation profiles obtained when no compressibility is involved.

The results suggest that the velocity of a wave, which is associated with the transport of a certain mass of CO2 along the permeable medium, is a function of the gas saturation, compressibility of the rock and fluids, and the pressure gradient. The results reveal that the wave velocity will only be a function of the gas saturation and pressure gradient if the compressibility of the rock is negligible compared to that of CO2. Hence, the waves’ velocity will only depend on saturation, as is for an incompressible flow system, when changes in pressure gradient are minimal.

Thus, this paper explains how fast a compressible CO2 plume will travel along the aquifers length. In practice, the fate of the injected CO2 plume is essential to determine the storage capacity of aquifers and to evaluate the risk associated with the CO2 sequestration projects.

Introduction
Despite extensive research on analytical modeling of CO2 sequestration in saline aquifers (Szulczewski et al., 2009; Juanes et al., 2010; Ghanbarnezhad et al., 2011), the gas always has been considered as an incompressible fluid. The method of characteristics (MOC) solution of the overall composition balance equation of CO2 is derived for one-dimensional (1D) two-phase two-component flow in the presence of compressibility. In the following study, the incompressible assumption is relaxed and compressibility is represented by constant values.